In the 1990's and early 2000's multiple authors began to explore geometric structure in optimal transport and its connection to fluid dynamics [1]}, [2]}, [3]}, [4]}.
Entropic regularization and the Sinkhorn algorithm, [5]}, led to even more computational tractability and spurred work in applying optimal transport to image analysis, [6]}, [7]}.
Semi-discrete optimal transport limits the class of distributions considered and simplifies the dual-problem to optimal transport.
These advantages fostered interest in new application domains and brought tools from computational geometry into the field [8]}, [9]}, [10]}, [11]}, [12]}, [13]}.
